Rationality of Hilbert series in noncommutative invariant theory

Rationality of Hilbert series in noncommutative invariant theory

It is a fundamental result in commutative algebra and invariant theory that a finitely generated graded module over a commutative finitely generated graded algebra has rational Hilbert series, and consequently the Hilbert series of the algebra of polynomial invariants of a group of linear transforma...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2017-08
Hauptverfasser: Domokos, M, Drensky, V
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Invariants
Linear transformations
Mathematical analysis
Polynomials
Rationality
Tensors
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Domokos, M
Drensky, V
description It is a fundamental result in commutative algebra and invariant theory that a finitely generated graded module over a commutative finitely generated graded algebra has rational Hilbert series, and consequently the Hilbert series of the algebra of polynomial invariants of a group of linear transformations is rational, whenever this algebra is finitely generated. This basic principle is applied here to prove rationality of Hilbert series of algebras of invariants that are neither commutative nor finitely generated. Our main focus is on linear groups acting on certain factor algebras of the tensor algebra that arise naturally in the theory of polynomial identities.
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2076176639</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2076176639</sourcerecordid><originalsourceid>FETCH-proquest_journals_20761766393</originalsourceid><addsrcrecordid>eNqNjUEKwjAQAIMgWLR_CHgupIlN9SaI0rN4L7FsMaXNanZb6O_twQd4GhgGZiUSbUyeHQ9ab0RK1CmltC11UZhEnO-OPQbXe54ltrLy_RMiS4LogaQPMmBocBhGXsIJFjO56F1gyS_AOO_EunU9QfrjVuxv18elyt4RPyMQ1x2OcRlQrVVp89JaczL_VV-bJTn0</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2076176639</pqid></control><display><type>article</type><title>Rationality of Hilbert series in noncommutative invariant theory</title><source>Free E- Journals</source><creator>Domokos, M ; Drensky, V</creator><creatorcontrib>Domokos, M ; Drensky, V</creatorcontrib><description>It is a fundamental result in commutative algebra and invariant theory that a finitely generated graded module over a commutative finitely generated graded algebra has rational Hilbert series, and consequently the Hilbert series of the algebra of polynomial invariants of a group of linear transformations is rational, whenever this algebra is finitely generated. This basic principle is applied here to prove rationality of Hilbert series of algebras of invariants that are neither commutative nor finitely generated. Our main focus is on linear groups acting on certain factor algebras of the tensor algebra that arise naturally in the theory of polynomial identities.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algebra ; Invariants ; Linear transformations ; Mathematical analysis ; Polynomials ; Rationality ; Tensors</subject><ispartof>arXiv.org, 2017-08</ispartof><rights>2017. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>776,780</link.rule.ids></links><search><creatorcontrib>Domokos, M</creatorcontrib><creatorcontrib>Drensky, V</creatorcontrib><title>Rationality of Hilbert series in noncommutative invariant theory</title><title>arXiv.org</title><description>It is a fundamental result in commutative algebra and invariant theory that a finitely generated graded module over a commutative finitely generated graded algebra has rational Hilbert series, and consequently the Hilbert series of the algebra of polynomial invariants of a group of linear transformations is rational, whenever this algebra is finitely generated. This basic principle is applied here to prove rationality of Hilbert series of algebras of invariants that are neither commutative nor finitely generated. Our main focus is on linear groups acting on certain factor algebras of the tensor algebra that arise naturally in the theory of polynomial identities.</description><subject>Algebra</subject><subject>Invariants</subject><subject>Linear transformations</subject><subject>Mathematical analysis</subject><subject>Polynomials</subject><subject>Rationality</subject><subject>Tensors</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNjUEKwjAQAIMgWLR_CHgupIlN9SaI0rN4L7FsMaXNanZb6O_twQd4GhgGZiUSbUyeHQ9ab0RK1CmltC11UZhEnO-OPQbXe54ltrLy_RMiS4LogaQPMmBocBhGXsIJFjO56F1gyS_AOO_EunU9QfrjVuxv18elyt4RPyMQ1x2OcRlQrVVp89JaczL_VV-bJTn0</recordid><startdate>20170821</startdate><enddate>20170821</enddate><creator>Domokos, M</creator><creator>Drensky, V</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20170821</creationdate><title>Rationality of Hilbert series in noncommutative invariant theory</title><author>Domokos, M ; Drensky, V</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20761766393</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Algebra</topic><topic>Invariants</topic><topic>Linear transformations</topic><topic>Mathematical analysis</topic><topic>Polynomials</topic><topic>Rationality</topic><topic>Tensors</topic><toplevel>online_resources</toplevel><creatorcontrib>Domokos, M</creatorcontrib><creatorcontrib>Drensky, V</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Domokos, M</au><au>Drensky, V</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Rationality of Hilbert series in noncommutative invariant theory</atitle><jtitle>arXiv.org</jtitle><date>2017-08-21</date><risdate>2017</risdate><eissn>2331-8422</eissn><abstract>It is a fundamental result in commutative algebra and invariant theory that a finitely generated graded module over a commutative finitely generated graded algebra has rational Hilbert series, and consequently the Hilbert series of the algebra of polynomial invariants of a group of linear transformations is rational, whenever this algebra is finitely generated. This basic principle is applied here to prove rationality of Hilbert series of algebras of invariants that are neither commutative nor finitely generated. Our main focus is on linear groups acting on certain factor algebras of the tensor algebra that arise naturally in the theory of polynomial identities.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2017-08
issn 2331-8422
language eng
recordid cdi_proquest_journals_2076176639
source Free E- Journals
subjects Algebra
Invariants
Linear transformations
Mathematical analysis
Polynomials
Rationality
Tensors
title Rationality of Hilbert series in noncommutative invariant theory
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-22T09%3A01%3A40IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Rationality%20of%20Hilbert%20series%20in%20noncommutative%20invariant%20theory&rft.jtitle=arXiv.org&rft.au=Domokos,%20M&rft.date=2017-08-21&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2076176639%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2076176639&rft_id=info:pmid/&rfr_iscdi=true